# Distribution of sum log(Irwin Hall distribution)

Let $$X_{ij} \, 1\leq i\leq m, 1\leq j \leq n$$ are uniform random variables (firstly assume them distributed on [0,1]), I want to know the pdf, mean and variance of $$\sum_{j=1}^n log(\sum_{i=1}^m X_{ij})$$, what if $$X_{ij}\sim U(a_i,b_i)$$?I have no idea. Please help me. Thanks a lot!

ps:see https://arxiv.org/pdf/math/0411298v1.pdf for results of sum of non-identical uniform variables $$U(c_i-a_i,c_i+a_i)$$.

• What is your personal work on the subject ? Do you know for example that for $n=1$ you have an exponential distribution ? What happens for $n=2$ ? Have you tried to simulate the law on a computer ? etc... Work hard on a question, then explain where you are blocked. – Jean Marie Mar 16 at 7:07